Earth Curvature Calculator

Accurately calculate the curvature you are supposed to see on the ball Earth.

DistanceCurvature
1 km0.00008 km = 0.08 meters
2 km0.00031 km = 0.31 meters
5 km0.00196 km = 1.96 meters
10 km0.00785 km = 7.85 meters
20 km0.03139 km = 31.39 meters
50 km0.19620 km = 196.20 meters
100 km0.78479 km = 784.79 meters
200 km3.13897 km = 3138.97 meters
500 km19.6101 km = 19610.09 meters
1000 km78.3196 km = 78319.62 meters

Explanation:

The Earth's radius (r) is 6371 km or 3959 miles, based on numbers from Wikipedia,
which gives a circumference (c)of c = 2 * π * r = 40 030 km

We wish to find the height (h) which is the drop in curvature over the distance (d)

Using the circumference we find that 1 kilometer has the angle
360° / 40 030 km = 0.009°. The angle (a) is then a = 0.009° * distance (d)

The derived formula h = r * (1 - cos a) is accurate for any distance (d)

curvature